Momentum - AP Physics 1

A ball of mass $m$ moves west at speed $v$ , and a second ball of mass $m$ moves east at speed $v$ . Which statement about their momenta is correct?
Answer: Their momentum magnitudes are equal, but directions are opposite This question examines momentum as a vector quantity for objects moving in opposite directions. Momentum p = mv is a vector, so direction matters: the westward ball has p₁ = m × (-v) = -mv, while the eastward ball has p₂ = m × (+v) = +mv. The momentum magnitudes are both |p| = mv, making them equal, but the directions are opposite (one negative, one positive). This means the momentum vectors are different even though their magnitudes are the same. Choice D incorrectly relates kinetic energy signs to momentum; kinetic energy is always positive regardless of direction. When objects have equal mass and speed but opposite directions, their momentum magnitudes are equal but their momentum vectors are opposite.
Object X and object Y move along the $x$ -axis. X has mass $m$ and velocity $-v$ ; Y has mass $m$ and velocity $+v$ . Which statement about their momenta is correct?
Answer: Their momenta are equal in magnitude and opposite in direction This question assesses understanding of momentum vectors in AP Physics 1. Momentum is the product of mass and velocity, and as a vector, it incorporates both magnitude and direction. Equal masses with equal speeds but opposite velocities yield momenta of equal magnitude but opposite directions. This is because p = m v and p = m (-v) are negatives of each other. A common distractor is choice D, which wrongly assumes equal speeds cancel momentum to zero, ignoring vector nature. To analyze such scenarios, assign signs based on a chosen positive direction and compare vector values.
A puck of mass $m$ moves in the $+x$ direction at speed $v$ . What is the direction of the puck's momentum?
Answer: In the $+x$ direction This problem tests understanding that momentum is a vector quantity. Momentum is defined as the product of mass and velocity ( $p = mv$ ), where velocity includes both speed and direction. Since the puck moves in the +x direction with velocity $ +v $, its momentum is $ p = m(+v) = +mv $. The positive sign indicates the momentum points in the $ +x $ direction, making the momentum vector point the same way as the velocity vector. Choice D incorrectly claims momentum has no direction, but momentum is always a vector. Remember that momentum always points in the same direction as velocity.
Object A has mass $3m$ and speed $v$ in the $-x$ direction. Object B has mass $m$ and speed $3v$ in the $+x$ direction. Which statement about their momenta is correct?
Answer: Their momentum magnitudes are equal, but directions are opposite This question tests calculating and comparing momentum vectors. Momentum equals mass times velocity (p = mv), including direction. Object A has momentum $p_A$ = (3m)(-v) = -3mv (negative indicates -x direction), giving magnitude | $p_A$ | = 3mv. Object B has momentum $p_B$ = (m)(+3v) = +3mv (positive indicates +x direction), giving magnitude | $p_B$ | = 3mv. Choice C incorrectly focuses only on speed without considering mass. Both objects have the same momentum magnitude (3mv) but opposite directions. When comparing momenta, calculate the full vector (including sign) first, then determine magnitude by taking the absolute value.
A $4.0\,\text{kg}$ glider moves at $+2.5\,\text{m/s}$ along the $x$ -axis. What is the direction of its momentum?
Answer: Positive $x$ direction This question assesses understanding of momentum direction in AP Physics 1. Momentum is a vector quantity calculated as the product of mass and velocity, sharing the same direction as the velocity vector. For motion along the x-axis, a positive velocity indicates positive x-direction for momentum. The direction is inherent to the vector nature of momentum, not perpendicular or undefined. A common distractor is choice A, which might appeal if one mistakenly reverses the sign of the given positive velocity. When determining momentum direction, always align it with the velocity vector's direction for transferable problem-solving.
A cart has momentum $-6\,\text{kg}\cdot\text{m/s}$ along the $x$ -axis. Which statement about its motion must be true?
Answer: The cart is moving in the $-x$ direction This problem tests interpreting negative momentum values. Momentum is mass times velocity (p = mv), and negative momentum indicates motion in the negative direction of the chosen axis. Given p = -6 kg·m/s along the x-axis, the negative sign tells us the cart moves in the -x direction (leftward). We cannot determine specific values of mass or speed from momentum alone, only their product equals 6 kg·m/s. Choice D is incorrect because negative momentum doesn't mean zero kinetic energy. When momentum is negative along an axis, the object must be moving in the negative direction of that axis.
A $6.0\,\text{kg}$ cart moves at $2.0\,\text{m/s}$ east. A second cart has momentum magnitude $12\,\text{kg}\cdot\text{m/s}$ . If it moves west, what is its momentum?
Answer: $-12\,\text{kg}\cdot\text{m/s}$ This question assesses understanding of momentum as a signed quantity in AP Physics 1. Momentum is the product of mass and velocity, with sign indicating direction (e.g., east positive, west negative). Magnitude is the absolute value, but the full momentum includes the sign. For the second cart moving west with magnitude 12, it is -12 kg m/s. A common distractor is choice A, which omits the negative sign for west direction. Assign a consistent positive direction and apply signs accordingly for vector quantities like momentum.
Two carts move along a line. Cart 1: mass $3m$, speed $v$ to the left. Cart 2: mass $m$ , speed $3v$ to the right. Which statement is true about momentum magnitudes?
Answer: They have equal momentum magnitude This question assesses understanding of momentum magnitude with opposite directions in AP Physics 1. Momentum is the product of mass and velocity, a vector with direction matching velocity. Magnitude ignores direction, so it's mass times speed for comparison. Cart 1's 3m times v equals 3m v, same as cart 2's m times 3v. A common distractor is choice D, which confuses equal kinetic energies (both 1.5 m v²) with momentum, but they are distinct. To solve, calculate magnitudes separately and compare, regardless of direction.
Two objects move along a line. Object $H$ has mass $m$ and velocity $+2v$ . Object $J$ has mass $2m$ and velocity $+v$ . How do their momentum magnitudes compare?
Answer: $|p_H|=|p_J|$ because both equal $2mv$ This question compares momentum magnitudes when objects have different mass-velocity combinations. Momentum magnitude is calculated as |p| = |m × v|, the absolute value of mass times velocity. Object H has momentum pH = m × 2v = 2mv (positive direction), so |pH| = 2mv. Object J has momentum pJ = 2m × v = 2mv (positive direction), so |pJ| = 2mv. Both momentum magnitudes equal 2mv, showing that doubling mass while halving velocity (or vice versa) maintains the same momentum magnitude. Choice D incorrectly mentions acceleration, which is irrelevant to momentum calculation. To compare momentum magnitudes, calculate m × v for each object and compare the results.
Object X has mass $m$ and speed $3v$ . Object Y has mass $3m$ and speed $v$ . Both move in the $+x$ direction. Which statement about momentum is correct?
Answer: $p_X = p_Y$ This problem tests understanding of the momentum formula p = mv. Momentum is the product of mass and velocity, where both factors contribute equally to the result. For object X: $p_X$ = m × 3v = 3mv. For object Y: $p_Y$ = 3m × v = 3mv. Since both products equal 3mv and both move in the +x direction, their momenta are equal. Choice D incorrectly assumes momentum depends only on speed, ignoring the role of mass. When comparing momenta, always calculate the full product of mass times velocity for each object.
Two identical balls each have mass $m$ . Ball 1 moves right at speed $v$ . Ball 2 moves right at speed $2v$ . How does Ball 2's momentum compare to Ball 1's? Motion is along one line.
Answer: Ball 2 has twice the momentum, in the same direction. This question evaluates the relationship between speed and momentum for identical masses in AP Physics 1. Momentum is the product of mass and velocity, so for equal masses, it scales directly with velocity magnitude and shares its direction. Ball 1 has momentum m v, while Ball 2 has m times 2v, doubling the momentum in the same direction. This demonstrates how momentum depends linearly on velocity when mass is constant. Choice C distracts by confusing momentum with kinetic energy, which scales with velocity squared. A transferable strategy is to compare momenta by computing p = m v for each object and noting proportionalities.
A block of mass $m$ moves right with speed $v$ . A second block of mass $\tfrac{m}{2}$ moves left with speed $2v$ . Which block has the greater momentum magnitude?
Answer: They have equal momentum magnitude This problem compares momentum magnitudes for objects moving in opposite directions. Momentum is mass times velocity (p = mv), where direction matters for the vector but not for magnitude comparison. First block: p₁ = m × v = mv (rightward). Second block: p₂ = (m/2) × 2v = mv (leftward). The magnitudes are |p₁| = mv and |p₂| = mv, which are equal. Choice D incorrectly relates momentum to kinetic energy, but these are different quantities with different formulas. To compare momentum magnitudes, calculate |mass × speed| for each object.
A cart of mass $4\,\text{kg}$ moves left with velocity $-3\,\text{m/s}$ along the $x$ -axis. What is the cart's momentum?
Answer: $-12\,\text{kg}\cdot\text{m/s}$ This problem tests momentum calculation with specific numerical values and direction. Momentum equals mass times velocity (p = mv), where velocity includes both magnitude and direction. Given m = 4 kg and v = -3 m/s (negative because leftward), we calculate p = 4 kg × (-3 m/s) = -12 kg·m/s. The negative sign indicates leftward motion along the x-axis. Choice C incorrectly multiplies 4 × 3 and adds a positive sign, ignoring the velocity's direction. Always include the velocity's sign when calculating momentum to preserve directional information.
A cart of mass $m$ moves with velocity $+v$ and has momentum $p$ . The cart later moves with velocity $-v$ (same speed). What is its momentum then?
Answer: $-p$ This problem tests how momentum changes when velocity reverses direction. Momentum is the product of mass and velocity (p = mv), and is a vector quantity that depends on direction. Initially, with velocity +v, momentum is p = m(+v) = +p. When velocity becomes -v (same speed, opposite direction), the new momentum is p' = m(-v) = -p. The magnitude remains the same, but the sign changes to indicate opposite direction. Choice C incorrectly suggests momentum becomes zero when only direction changes. Remember that reversing velocity direction reverses momentum direction while preserving magnitude.
A puck of mass $0.50\,\text{kg}$ slides to the right at $4.0\,\text{m/s}$ . What are the magnitude and direction of its momentum?
Answer: $2.0\,\text{kg}\cdot\text{m/s}$ to the right This question requires calculating momentum using the fundamental relationship p = mv. Momentum is defined as the product of an object's mass and velocity, with units of kg·m/s, and it's a vector quantity that has both magnitude and direction. For the puck: p = (0.50 kg) × (4.0 m/s) = 2.0 kg·m/s, and since the puck moves to the right, the momentum direction is also to the right. The magnitude is 2.0 kg·m/s and the direction is rightward. Choice D incorrectly uses units of Joules (J), which are units of energy, not momentum. To find momentum, always multiply mass times velocity and preserve the direction of motion.
On a straight track, cart $A$ has mass $m$ and moves east at speed $3v$ . Cart $B$ has mass $2m$ and moves west at speed $v$ . Taking east as positive, which cart has the greater momentum magnitude?
Answer: Cart $A$ , because $|p_A|=3mv$ and $|p_B|=2mv$ This question tests understanding of momentum magnitude in one-dimensional motion. Momentum is the product of mass and velocity, calculated as p = mv, where direction matters for the full vector but magnitude is the absolute value. Cart A has momentum pA = m × 3v = 3mv eastward (positive), while Cart B has momentum pB = 2m × (-v) = -2mv (westward, negative). The magnitude of Cart A's momentum is |pA| = 3mv, and the magnitude of Cart B's momentum is |pB| = 2mv. Choice B incorrectly focuses only on mass without considering velocity. When comparing momentum magnitudes, always calculate the full product m × v before taking absolute values.
A cart of mass $3.0\,\text{kg}$ moves in the $+x$ direction at $2.0\,\text{m/s}$ . A second cart has momentum of equal magnitude. What must be true about the second cart's momentum direction? All motion is one-dimensional.
Answer: It could be in either the $+x$ or $-x$ direction. This question probes the possible directions of momentum given equal magnitudes in AP Physics 1. Momentum is the vector product of mass and velocity, allowing equal magnitudes in either direction depending on velocity sign. The first cart's momentum is 3 kg times 2 m/s positive, magnitude 6 kg m/s; the second could match this positively or negatively. This shows direction is not fixed by magnitude alone. Choice D incorrectly assumes equal magnitudes imply zero momentum, misunderstanding vector nature. A transferable strategy is to solve for possible velocities that yield the required momentum magnitude, considering both directions.
Two carts move along the $x$ -axis. Cart A has mass $m$ and moves right at speed $2v$ . Cart B has mass $2m$ and moves left at speed $v$ . Which statement correctly compares their momenta? Assume right is the positive $x$ direction and ignore any interactions.
Answer: The carts have equal momentum magnitude but opposite directions. This question tests the concept of comparing momenta of objects with different masses and velocities in AP Physics 1. Momentum is a vector quantity defined as the product of an object's mass and its velocity, where velocity includes both speed and direction. In one dimension, the direction is indicated by the sign, with positive typically representing rightward motion. Thus, for Cart A, momentum is m times 2v positive, and for Cart B, it is 2m times -v, resulting in equal magnitudes but opposite directions. A common distractor like choice A incorrectly prioritizes speed over the mass-velocity product. A transferable strategy is to always calculate momentum as p = m v, accounting for signs, before comparing magnitudes or directions.
Two carts move along the $x$ -axis. Cart $C$ has mass $3m$ and velocity $+v$ . Cart $D$ has mass $m$ and velocity $-3v$ . How do their momentum directions compare?
Answer: The momenta point in opposite directions This question tests understanding of momentum as a vector quantity with direction. Momentum p = mv is a vector, meaning it has both magnitude and direction determined by the velocity's direction. Cart C has momentum pC = 3m × (+v) = +3mv, pointing in the positive x-direction. Cart D has momentum pD = m × (-3v) = -3mv, pointing in the negative x-direction. Since one momentum is positive and the other is negative, they point in opposite directions along the x-axis. Choice D incorrectly suggests that equal speeds eliminate momentum, confusing speed (scalar) with velocity (vector). Remember that momentum direction always follows velocity direction, regardless of mass differences.
Along one dimension, object P has mass $m$ and speed $2v$ ; object Q has mass $4m$ and speed $\tfrac{v}{2}$ , both moving right. Which has greater momentum magnitude?
Answer: They have equal momentum magnitude This question assesses understanding of equal momentum magnitudes in AP Physics 1. Momentum is the vector product of mass and velocity, with magnitude mass times speed. Both objects move right, so directions are the same. P's m times 2v equals 2m v, matching Q's 4m times v/2. A common distractor is choice D, which mixes up momentum with kinetic energy (P has 2m v², Q has m v²). For such comparisons, focus solely on the m v product and verify calculations step-by-step.

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